Question: Solve for $x$ and $y$ using elimination. ${4x-y = 12}$ ${-5x+y = -17}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {4x-y = 12}\thinspace$ to find $y$ ${4}{(5)}{ - y = 12}$ $20-y = 12$ $20{-20} - y = 12{-20}$ $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ You can also plug ${x = 5}$ into $\thinspace {-5x+y = -17}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ + y = -17}$ ${y = 8}$